一种适用于电介质中的电磁学的良定表面电流和电荷系统
A well-posed surface currents and charges system for electromagnetism in dielectric media
AI总结：
本文提出了一种新的表面积分方程（SIE）形式，该形式在特定函数空间中具有身份加紧致运算符形式，且在所有频率下均良定，并在低频下保持稳定。
摘要：
自由空间Maxwell电介质问题可以被减少为一个表面积分方程（SIE）系统。使用SIE系统来解决Maxwell电介质问题的数值方法具有两个关键优势：首先，在无穷远处的辐射条件被精确满足，其次不需要人工定义截断域。因此，这些SIE系统在物理学、电气工程和数学中引起了广泛兴趣，并随着时间的推移提出了许多SIE方法。在本文中，我们介绍了一种新的SIE方法，该方法具有理想的运算符形式，即身份加紧致，是良定的，并且在频率趋于零时仍保持良好条件。该方法中的未知数是电介质体边界上的三维向量场。本文研究的SIE来源于之前由部分作者~\cite{ganesh2014all}开发的公式。我们的初始方法利用线性约束来获得所有频率下的唯一可解系统。本文中引入并分析的新SIE结合了\cite{ganesh2014all}中的积分方程和新的约束。我们证明了新系统在特定函数空间中具有身份加紧致运算符形式，并在所有频率下证明了新SIE的良定性，并证明了新SIE在低频下的稳定性。
英文摘要：
The free space Maxwell dielectric problem can be reduced to a system of surface integral equations (SIE). A numerical formulation for the Maxwell dielectric problem using an SIE system presents two key advantages: first, the radiation condition at infinity is exactly satisfied, and second, there is no need to artificially define a truncated domain. Consequently, these SIE systems have generated much interest in physics, electrical engineering, and mathematics, and many SIE formulations have been proposed over time. In this article we introduce a new SIE formulation which is in the desirable operator form identity plus compact, is well-posed, and remains well-conditioned as the frequency tends to zero. The unknowns in the formulation are three dimensional vector fields on the boundary of the dielectric body. The SIE studied in this paper is derived from a formulation developed in earlier work by some of the authors~\cite{ganesh2014all}. Our initial formulation utilized linear constraints to obtain a uniquely solvable system for all frequencies. The new SIE introduced and analyzed in this article combines the integral equations from \cite{ganesh2014all} with new constraints. We show that the new system is in the operator form identity plus compact in a particular functional space, and we prove well-posedness at all frequencies and low-frequency stability of the new SIE.
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